Why do we tax income? Or to put it another way, why do we use income as a basis for taxation?
(Or for that matter, why do we use anything else, whether it's whiskey, windows, or chewing gum. Or real property owned? Or imports? Or consumption? Or payroll? Or lottery tickets?)
1) Because we can. (This is a matter of practicality and available technology. There was a time when taxing income wasn't as practical as it is now, because the economy was largely a non-cash informal economy.) It's also a matter of how easy or not it is for people to escape paying taxes. For example, relatively few cities impose income taxes on their residents, because in most cases, there are good substitute places to live nearby where people can escape paying the income tax. It's easier for a national government to impose a substantial income tax than a state government, and easier for a state government to impose an income tax than a local government. Economists discuss the ease with which people can escape being part of the tax base using the notion of "elasticity" as a way to measure the responsiveness of behavior to taxation. In general, it is easier to tax an inelastic tax base than an elastic tax base.
2) Because the tax base fits with some theory of taxation criterion such as
--ability to pay criterion => people who have greater ability to pay for government services should in fact pay more
For example, perhaps, people with more whiskey, windows, chewing gum, income, real property, imports, consumption, payroll, etc. have a greater ability to pay, in which case that tax base might be a good one. Obviously, income has a strong claim to being a good basis for taxaton on the "ability to pay" theory of tax criterion.
--benefit theory of taxation => people who benefit more from government services should pay more for them
The benefit theory of taxation has been used to justify property as a tax base (e.g, people with more property benefit more from public services such as police and fire departments, the criminal justice system, etc.) One could make a similar argument about income--that high income people benefit more from government services than low income people, and therefore ought to pay more tax on that account. Certainly, both Warren Buffett and Bill Gates have acknowledged some validity to that argument. The benefit theory of taxation has also been used to justify gas taxes, since gas usage is, at least somewhat, correlated with highway usage.
--externality taxation (also known as Pigovian taxation) => this theory says we should tax things that society wants to discourage, because the free market system does not impose the full social costs of certain activities
The externality theory of taxation has been used to justify "sin taxes" of a variety of sorts: taxes on whiskey (external social costs of drunk driving, for example) and chewing gum (think of the external social costs of used chewing gum stuck in unfortunate places!), Governor Paterson's new proposed soda tax (because obesity and, more generally, poor eating habits are associated with higher health costs, which the rest of society indirectly shares through health insurance costs). Taxes on pollution (or proxies for pollution, such as gas usage) are examples of Pigovian taxation.